Symplectic effective field theory for nuclear structure studies

A symplectic effective field theory that unveils the observed emergence of symplectic symmetry in atomic nuclei is advanced. Specifically, starting from a simple extension of the harmonic-oscillator Lagrangian, an effective field theory applied against symplectic basis states is shown to yield a Hamiltonian system with one fitted parameter. The scale of the system can be determined self-consistently as the ratio of the average volume of a nucleus assumed to be spherical to its volume as determined by the average number of oscillator quanta, which is stretched by the fact that the plane-wave solution satisfies the equations of motion at every order without the need for perturbative corrections. As an application of the theory, results for ${}^{20}\mathrm{Ne}$, ${}^{22}\mathrm{Ne}$, and ${}^{22}\mathrm{Mg}$ are presented that yield energy spectra, $B\left(E2\right)$ values, and matter radii in good agreement with experimentally measured results.

Figure 1

The energy spectrum and $B\left(E2\right)$ values of the 48.5(8,0) symplectic irrep for ${}^{20}\mathrm{Ne}$ using the SpEFT in a $N_{\max }=12$ model space (EFT) compared with experimental data (Expt.) [42]. $B\left(E2\right)$ values are in W.u.

Figure 2

SpEFT energy spectrum and $B\left(E2\right)$ values of the 55.5(8,2) symplectic irrep for ${}^{22}\mathrm{Ne}$ in a $N_{\max }=12$ model space compared with experimental data (Expt.) [43]. $B\left(E2\right)$ values are in W.u.

Figure 3

SpEFT energy spectrum and $B\left(E2\right)$ values of the 55.5(8,2) symplectic irrep for ${}^{22}\mathrm{Mg}$ in a $N_{\max }=12$ model space compared with experimental data (Expt.) [43]. $B\left(E2\right)$ values are in W.u.